An Approach of Correlation Inter-variable Modeling with Limited Data for Inter-Bus Transformer Weather Sensitive Loading Prediction

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1 International Journal on Electrical Engineering and Informatics Volume 4, Number 4, December 0 An Approach of Correlation Inter-variable Modeling with Limited Data for Inter-Bus Transformer Weather Sensitive Loading Prediction Fitriana and Nanang Hariyanto Research Center for Electrical Engineering and Mechatronics Indonesian Institute of Sciences Komplek LIPI Gedung 0 Jalan Cisitu /54 D Dago Bandung 4035 Indonesia School of Electrical Engineering and Informatics, Institut Teknologi Bandung Gedung Kerma PLN-ITB Lt. Jalan Ganesha No.0 Bandung 403 Indonesia fitrisalsa@gmail.com, nanang.hariyanto@stei.itb.ac.id Abstract: This paper deals with a method to determine short-term loading estimation of inter-bus transformers based only a limited data of variables. A grey predicting approach is implemented in this paper to solve dynamic short term load forecasting affected by the climate changes in Indonesian EHV grid, as provided by Jawa Bali Control Center. A dynamic forecasting model is needed due to the uncertain nature of the load predicting process specifically when load changes is correlated with the external effect. Traditional GM (,) as basic model is presented to compare with the correlation inter-variable model in grey method for inter-bus loading transformers loading conditions refer to the temperature variation pattern during only the year 009. GM(,) model denotes the correlation and relationship of hourly load demand affected to the (two) tropical seasons, in this case by using local ambient temperature as dynamic variable. The daily load curve for Cawang and Cibatu distribution areas, as representing big local substations in Indonesia spatially, was used to validate the models. The model adequacy and weekly forecasting result had indicated a good and justified grade in error diagnostic checking (MAPE) in each location. Keywords: grey dynamic forecasting model, correlation inter-variable model, ambient temperature records, local load profiles. Introduction Rapid information and development of new theories of systems science have become an important part of modern science and technology, especially in research of uncertainty system. There are several theories how to handle uncertain data: fuzzy logic, system identification, dimensional analysis and Grey System Theory (GST). GST is the one of the most important research of uncertainty system that realizes the correct description and effective supervision in operation action and evolution law of system, mainly through generating, exploring and extracting valuable information from a little part known information to predict the unknown information value, where appeared initially in early 980 by J. Deng []. In grey systems, the information have partially known and partially unknown parameters especially useful, when the complete set of factors involved in the system s behaviour is unclear, () when the relationships of system factors to the system s behaviour and interrelationships among factors are uncertain, (3) when the system behaviour is too complex to determine completely, or (4) when only limited information or time series data on system behaviour is available. The essential scopes of GST encompass in research methods about: grey relational space, grey generating space, grey forecasting, grey decision making, grey control, grey mathematics and grey theory as base []. In real system, daily load requirement would change in real time due to uncertainty load behaviour in electric power systems. National State Electricity Company in Indonesia (PLN) have developed load forecasting based on coefficient method to support its operation and Received: June th, 0. Accepted: December 9 th, 0 646

2 Fitriana, et al. control planning []. It have been implemented only for a high and macro-scale data in Jawa Bali load systems using minimum 3-5 years past data. Unfortunately, its method do not accommodate the real relationship between daily loads and many weather variables such as ambient temperature, relative humidity, wind speed, etc. Regarding the changing climate in tropical area Indonesia, the electricity demand also should be predicted by extrapolating a predetermined relationship between the load and its influential variables - namely, time and/or weather-sensitive, toward short-term or long-term load forecasting. This paper propose a model scheme for quantifying the relationship between the load and ambient temperature data information specific in certain area and the use of a suitable parameter estimation technique obtained from Grey Forecasting Method (GFM) in accordance with the schemes. However, due having only a little temperature data and smaller case coverage, only two main schemes of the GFM as grey dynamic models, abbreviated as GM (,) and GM (,), will be implemented [3]. It was used to predict of short term electric demand that includes certain location (as condition referred to where ) as one of its main elements, in addition to load magnitude (how much) and seasonal or temporal (when) characteristics, so the method have been implemented as spatial load forecasting [9]. As study cases, (two) inter-bus transformers loading conditions in Jakarta area had been chosen to improve the grey predicting approach in power/energy systems. The application GM(,) combined model considering the influencing factor of load to forecast a day-ahead electricity prices had been implemented in China [6], and many additional methods also can be adopted to obtain optimal coefficient and enhance the estimation validation index [4],[5]. However, new contribution in this paper was grey theory implementation in loading estimation analysis with incomplete data and correlate (two) inter-variables, where known the specific condition in one area which are slightly different with another, inclusive weather effects, power consumption pattern of its customer, sudden network change due to operation strategies requirement. The conformity of correlation coefficient based on the profiling of data information has developed a grey model scheme appropriate in specific area representing tropical climate condition. Hence, the hybrid grey model developed by [5] could not be applied in tropical climate condition at all, so the GM(,) method schemes mentioned in [4] did not appropriate to all cases.. Grey Estimation Methods In grey system theory for analysing non-linier systems, a differential model called the Grey Model (GM) only need to use at least 4 (four) samples to model and replace difference modelling in vast quantities of data [3]. A. GM(,) Model The series processed is ordered to be the GM (,) modelling sequence, denote the original data sequence as follows: {, (), (3)..., ( n) } = The AGO formation of ( k) 0, k =,,3,..., n) is generated to the first order series ( k), ( k) is defined as follows: { }{ } {, (), (3),..., ( n) } = () The above two series meet the following relationship as follows: =, and 647

3 An Approach of Correlation Inter-variable Modeling with Limited Data k ( ) k = x ( m), k =,,3,..., n (3) ( ) m The GM(,) model can be constructed by establishing a first order differential equation for as follows: ( k) d ( k) + a dt = b where, a and b are the parameters to be determined, (4) is scattered available as follows: [ ( k + ) + ( k) ] = b, ( k =,,3,..., ) ( k + ) + a n (5) Then, (5) can be expressed by using the matrix form Y n = Ba, where [ + ()] [ + ] B = () (3) M M [ ( n ) + ( n) ] () (3) Y n = M ( n) T a = ( a, b) (6) In (5), the unknown variable is only a and b, but there are n- numbers of equations, it is obviously no solution, but the least square method can be used to derive least square solution. The matrix equation can be rewritten as follows: Y n = Baˆ + ε, ε is the error terms, ˆ T min Yn Ba = min( Yn Baˆ) ( Yn Baˆ) the derivation is ordered by using the matrix, it is available as follows: a aˆ T T = ( B B) B Yn = (7) b (7) is into (4), the time response function can be solved as follows: b b ˆ (0 ( t) = ) e at + a (8) a The scattered type as the time response sequence of grey differential equation is given by (0) is the basic model of the grey forecasting GM (,). (4) ( k + ) = ˆ (0 ) b e a ak + b a (9) ˆ ˆ ( ) ( ) ˆ ( k + = k + ) ( k) (0) Equation (0) is the specific formula of the GM (,) model of grey prediction. Then the meaning of the symbol GM(,) is given as follows [3] and so on for other models. 648

4 Fitriana, et al. G Grey M Model (, st Order ) One Variable With GM (,) model for demand forecasting, but the accuracy of forecasting model is also need to be checked so that the future value predicted have a higher credibility. Residual test as follows: ( ) ( ) ˆ ε k = k ( k ) with absolute error in percentage (MAPE) and Δ = ε ( k) / ( k) [7]. B. GM(,) Model One kind of the grey relationship model in grey theory is GM(,N), where the data can be separated into two sequences, i.e. one major sequence factor, which is the sequence that masters the systems represent such as equation ; and N- influencing sequence factors, which are the sequences that influence the systems. The major sequence factor and its sequence factors can be defined as follows: M 3 = = N = {, (), (3),..., ( n) } {, (), (3),..., ( n) } {, (), (3),..., ( n) } 3 N N N N () where N is defined as the original sequence number. Subjecting these N- sequences to AGO as in (3) obtain the sequences. N After these sequences are subjected to the Accumulating Generation Operation (AGO), refer to equation (3), the following sequences obtained. The grey differential equation of N GM(,N) model is [3] N i i= d ( k) + a ( k) = b i ( k) dt () where a is the develop factor and b i as the driving terms which is the relationship weighting factors. So, the parameter vector defined in equation (6) can be solved where: T T T aˆ = [ a, b, b,..., b ] = ( B B B Y N ) (3) Which, B is a matrix derived from the matrix equation representing the grey equation in (). B = [ + ()] [ () + (3)] M () (3) N () (3) N M [ ( n ) + ( n) ] ( n) ( n) L N (4) 649

5 An Approach of Correlation Inter-variable Modeling with Limited Data Then the approximate time response sequence of GM(,N) equation is written as ˆ N N ( ( ) ( ) ak k + = ) + + ( + ) b i i k e b ii k (5) a a i= i= where is taken to be. Then the restoration of Inverse AGO will use equation (0). Summarizing the above GM(,N) model, the grey system model can be illustrated as Figure, where the system input is influencing sequences and the system output is major sequence. By utilizing relational factors and GM(,N) model, we can construct the function of the input and output sequences to furthermore understand the input-output relationship. Relational factor b Relational factor 3... b... GM(,N) Major factor Relational factor b N Figure. Block Diagram of Grey Relationship Analysis In the above mentioned GM (, N) model, we used GM (,) to correlate the relationship between the two sequences derived in problem statement i.e. load and ambient temperature data samples in certain location. To correlate the relationship between the two sequences as inter-variable derived in problem statement (load and ambient temperature data samples in certain location), we use GM (,), pronounced Grey Model st Order Two Variables [3]. Then the grey differential equation of GM (, ) model [3] is defined as follows: dx + ax = bx (6) dt where a is the develop factor and b i is the relationship weighting factors. The matrix equation refer to the equation (3) and (4) can be rewritten as GM (,) model and the parameter vector can be solved using the following solution. () Z () ( (3) Z (3) = (3) a M M b ( n) Z ( n) ( n) where the value of Z (n) can be derived by: (7) z ( k) = α x ( k) + ( α ) x ( k ), k=,3,..., n (8) where α is the production coefficient of background value as one of solution parameter of the grey differential equation. Then, the approximate time response sequence of GM (, ) can be written as follows: 650

6 Fitriana, et al. x ˆ ( ) ( k) x b a( k ) b = x ( k) e a + x ( k) a (9) where is taken to be. Finally the restoration of Inverse AGO will use equation (0) below. ˆ ( ˆ k + ) = ( k ˆ + ) ( k) (0) 3. The Profiling of Load Models The sample data in this study are based on the historical loading of inter-bus transformers (IBT) and ambient temperature information in (two) local substations in Jakarta area, i.e.: Cawang substation in 009, only data until September 8, 009 when IBT fail loading in there, and Cibatu substation with 009 data records from January until December 3, 009. Temperatur e Profile in Cawang ( C) Dry Season Rain Season Hour 800 Daily Load Curve in Cawang (MW) Dry Season Rain Season Hour Figure. Profile of Weather-Sensitive Daily Loads in Cawang 65

7 An Approach of Correlation Inter-variable Modeling with Limited Data Through this information, it divide the data into weekday, weekend, and separated holiday data for determining GM(,) and GM (,) models. This data was managed referring to the threshold values scheme using appoint technique [4]. Actually there are two main tropical season in Indonesia, dry season (from April to Augusts) and rainy season (from November to February). But climate changes effects have distracted existing period of each season, hence for similarity the data schemes of Cawang and Cibatu have been adapted in accordance with weather tendencies and have been used as training data, which was divided into weathersensitive loads and non-weather sensitive loads. Figure 3. Monthly Box-Plot Distribution of Weather-Sensitive Load in Cawang 65

8 Fitriana, et al. After profiling data, it was found that daily load curve of each day in Cawang in one week not be similar, as well as in Cibatu. But ambient temperature patterns always similar in a week for same season. The clustering tendency of daily load distribution in specific location should be compared with the trend of ambient temperature above normal, and then a correlation between load increments due to seasonal changes was represented by the increment of ambient temperature during the dry season. From Figure, the effect of seasonal changes have been faced on the average loading increase in that location, so the linear correlation states affected temperature and load model can be used to determine the sensitivity of IBT loading. The abnormal loading conditions in Cawang in 009 have been described using box-plot to find the monthly loading distribution. It was used as boundary of the data sampling that represent each IBT loading condition in certain season, as described in Figure 3. The daily load pattern curve in Cawang dominated by business customers and commercial linkages shows the correlation between the load and ambient temperature in site. As boundary, correlation modelling in Cawang for the dry season occurs from March to September and for rainy season occurs from January to February. Using the same profiling method, the temperature affected by IBT loading in Cibatu was determined and form weather sensitive load modeling pattern which the dry season occurs from March to October. Overall the load increase pattern due to the temperature effect in Cawang occurs starting at hour 7 to 8, who dominated the business customer activity (as representation of the commercial load profile), while in Cibatu suggests the contribution of industrial customers (represented the industry load profile) with mid-day load fluctuation. 4. Proposed Model Scheme Based on Correlation Inter-variable In this paper, daily day-ahead load in MW distributed in Cawang and Cibatu are selected to forecast and validate the performance of the common Grey estimation model. i.e. GM(,) and GM(,). Each model was applied to the same hours and the same days matched with the particular season to find the output coefficients therein. In general, variables that act upon the system of interest should be external or predefined. The GM(,) model is a single sequence modelling, which makes use of only the system s behaviour sequence, represented by output sequence or background values, without considering any external acting sequences represented by some input sequences or driving quantities as well as in GM(,N) model [3]. The parameters (-a) and (b) mentioned in (9) and (9) are called the development coefficient and grey action quantity, respectively. The parameter (-a) reflects development states of ˆ and ˆ and the grey action quantity in GM(,) is a value derived from the background values contained in column of matrix B in (6). Interestingly in GM(,N) model, (-a) still represent the development coefficient of the system, but bi i ( k) is called the driving term which ( b i ) reflect the driving coefficients. It would be different among (b) in GM(,) with ( b i ) in GM(,) which had been used in this paper. All b i parameters derived from simulation in each season was used to compare the impact correlations of daily weather trend and daily load curve in different areas, where shown in Table. SEASON Table. Correlation Coefficient Comparison in Cawang Driving Parameter or Model Control Variable ( b i ) MON TUE WED THU FRI SAT SUN DRY RAIN

9 An Approach of Correlation Inter-variable Modeling with Limited Data Table. Correlation Coefficient Comparison in Cibatu SEASON Driving Parameter or Model Control Variable ( b i ) MON TUE WED THU FRI SAT SUN DRY RAINY In the item of Monday until Sunday as shown in Table, it can be seen the average correlation coefficients aggregated for 4 hours in all days of week. The average driving coefficient in all Saturday and Sunday (weekend period) throughout the dry season had indicated lower value rather than Monday until Thursday (workday period), as shown in Figure 5. Whereas daily temperature had the similar distribution in all days of week during the dry season (Figure 4). Likewise in period of the rainy season, as shown in Figure 6, temperature tendency of each day in a week may be similar, but it had lower value compared than temperature tendency during dry season. The same trend also occurred by comparing the driving coefficient during dry season (Figure 5) with rainy season (Figure 7). Figure 4. Ambient Temperature Distribution through Dry Season 654

10 Fitriana, et al. Figure 5. Correlation Coefficient in GM(,) for All Days of Week through Dry Season Figure 6. Ambient Temperature Distribution through Rainy Season 655

11 An Approach of Correlation Inter-variable Modeling with Limited Data Figure 7. Correlation Coefficient in GM(,) for All Days of Week in through Rainy Season Based on the correlations, it can conclude that the correlation between load distribution and temperature in weekend period did not corresponded with their daily temperature distribution spatially. However, the driving coefficient derived in Cibatu substation had given similar results with Cawang, as shown in Table. In order to conform each correlation factors spatially, it is necessary to combine grey model appropriate with the daily temperature patterns in this locations and the model should not ignore the power consumption pattern refer to them. Hence, Jakarta area which are dominated by business and industrial consumers, GM(,) would be applicable to forecast the power demand only in workday period, and GM(,) could be implemented in this period. The proposed grey schemes would be implemented throughout the year in Jakarta area spatially, both in dry season and rainy season. As noticed in Jakarta area, the special holiday with a long period which gives a significant effect on daily load curve are only in Ied-Fitri holiday (IFH). From historical data known that IFH holiday period until nearly a week continuously with lower demand than other holiday usually. Because lack of data, we cannot estimate the grey model of IFH period for Cawang. But Cibatu substation had a adequate data in 009, so we also studied to implement and compare whether suitable grey model for IFH period in Cawang using, GM(,) or GM(,). Caused by the temperature data obtained only a year, in 009, estimation model could not been executed to the other types of holiday had one day off, called National holiday such as Waisak Day, Chinese New Year, Christmas Day, Independence Day, etc. in which almost totally 5 types in a year. 5. Analysis and Test Validation Accordance with the proposed schemes, the MAPE of Grey model using data profiling was compared with only GM(,), as shown in Table 3 and Table 4. The items presented in the tables can compare implementation of grey modelling in particular season for all substations represented in Jakarta area. The modelling result of GM(,) in Saturday and Sunday produced average error greather than the other days, such as a smaller correlation coefficient result in Table and. This result has reinforced the model scheme of loading estimation in (two) area proposed. 656

12 Fitriana, et al. Hence, it can be seen that implementation GM(,) only in workday period has lower error rather than the model scheme in all day consistently, likewise the model precision in Cawang has better accuracy compared to Cibatu. The adequacy of proposed Grey model were tested through the diagnostic checking of residuals, with MAPE values were below 0%, which were also included justified grade in model adequacy limit, as defined in [3]. Table 3. Model Error Comparison in Dry Season Profiling MAPE (%) GM(,) Proposed Model Scheme CAWANG CIBATU CAWANG CIBATU MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY AVERAGE ERROR Table 4. Model Error Comparison in Rainy Season Profiling MAPE (%) GM(,) Proposed Model Scheme CAWANG CIBATU CAWANG CIBATU MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDAY AVERAGE ERROR For Jakarta area spatially, the proposed grey model scheme was used to predict one-hour ahead of load value in each location during the same season. From equation (9) and (9), there were 4 hours x 7 days x 4 variable values that would produce 4 sequence sets which are capable for establishing 4 GM(,) models to predict one-workday ahead daily loads and 4 GM(,) models to predict one-weekday ahead daily load, respectively in a week. In workday forecasting, one temperature value must be included to increase the last number of AGO simulated, ( ) as initial value in (9). k 657

13 An Approach of Correlation Inter-variable Modeling with Limited Data It is practical to present only a representative subset of the load forecasting test results. During dry season, both the forecasted daily load curve were drawn, as shown in Figure 8 and Figure 9, on Sunday September 6, 009 (representing weekend) and on Monday September 7, 009 (representing workday) for Cawang and Cibatu, respectively. Figure 0 represent daily load curve during rainy season. From these figures, it can be seen that the predicted load agree with the observed value quite well, and still had forecasting error value (MAPE) under the limit of adequacy. 900 SUNDAY SEPTEMBER 6, 009 Cawang Daily Load (MW) Forecasting Actual Hour 900 MONDAY SEPTEMBER 7, 009 Cawaang Daily Load (MW) Forecasting Actual Hour Figure 8. CAWANG Daily Load Curve during Dry Season 658

14 Fitriana, et al. Cibatu Daily Load (MW) SUNDAY SEPTEMBER 6, 009 Forecasting Actual Hour Cibatu Daily Load (MW) MONDAY SEPTEMBER 7, 009 Forecasting Actual Hour Figure 9. CIBATU Daily Load Curve during Dry Season 659

15 An Approach of Correlation Inter-variable Modeling with Limited Data 900 SUNDAY FEBRUARY, Cawang Daily Load (MW) Forecasting Actual Hour 900 MONDAY FEBRUARY 3, Cawang Daily Load (MW) Forecasting Actual Hour Figure 0. CAWANG Daily Load Curve during Rainy Season Finally, we had listed one-week ahead load forecasting error of the test results from Sunday 6 th September to Saturday th September in 009 throughout dry season as described in Table 5 for each location, respectively. Likewise the weekly load forecasting error had been conducted from Sunday th February until Saturday 8 th February during rainy season in 009, as listed in Table

16 Fitriana, et al. Table 5. Weekly Load Estimation Test Result During Dry Season Location Forecasting Validation Error (%) MON TUE WED THU FRI SAT SUN Test Error Cawang Cibatu Table 6. Weekly Load Estimation Test Result During Rainy Season Forecasting Validation Error (%) MON TUE WED THU FRI SAT SUN Test Error Cawang Cibatu Conclusions This paper had proposed the combination grey model to estimate the correlation intervariable in specific location, which was based on GM(,) to predict one-workday ahead and one-weekend loading distributed in each location, respectively. GM(,) more appropriately used because load demand was correlated with temperature rise only in Monday until Friday, whilst not in Saturday and Sunday. It also concluded that the load prediction model in Jakarta area more influenced by energy consumption pattern and the most dominant type of consumer. Obviously, the adequacy of the models had shown a good grade when their error diagnostic were checked, with average error level still under 0%. If there are an incidence occurs as abnormal distribution operation strategies from distribution control center, i.e. sudden network reconfiguration for maneuver operations, these forecasting models will not be feasible numerically. The proposed scheme was not also applicable to any holiday factor. Hence in the next study it may be possible that the model by adding a factor, will affect the holiday factor added to the final prediction results. Futhermore the model performance improvement will also been conducted to generate the least minimum prediction error. Acknowledgment Authors thankful to Jawa Bali Load Control and Operator Center (PT. PLN P3B Gandul) and all of the project team as part of UI and ITB joint project in 00. References [] J. Deng, Introduction to Grey System Theory, The Journal of Grey System, Vol., No., pp. -4, 989. [] E. Wahyudi. Pembentukan Model Beban dalam Satu Tahun, PLN P3B Gandul, 00. [3] S. Liu, Y. Lin. Grey Information Theory and Practical Applications. ser. Advanced Information and Knowledge Processing. Verlag, London: Springer, 006. [4] Z. L. Gaing, R. C. Leou. Optimal Grey Topological Predicting Approach to Short-term Load Forecasting in Power System, IEEE Trans. on Power Systems, 00. [5] W. Li, Z. H. Han. Application of Improved Grey Prediction Model for Power Load Forecasting, IEEE Trans. on Power Systems, 008. [6] R. Wang, GM(,) Forecasting Method for Day-ahead Electricity Price Based on Moving Average and Particle Swarm Optimization, in Proc.6th International Conf. on Natural Computation, ICNC, 00. [7] E. Kayacan, B. Ulutas, O. Kaynak, Grey system theory-based models in time series prediction, Elsevier Journal in Expert Systems with Applications, vol. 37 p ,

17 An Approach of Correlation Inter-variable Modeling with Limited Data [8] H. T. Yang, T. C. Liang, K. R. Shih, C. L. Huang. Power System Yearly Peak Load Forecasting: A Grey System Modeling Approach, IEEE Catalogue No. 95TH830, 995. [9] Y. Sabri, Hariyanto, Fitriana, " Spatial Short-Term Load Forecasting using Grey Dynamic Model Specific in Tropical Area", International Proceeding of 0 International Conference on Electrical Engineering and Informatics, p. 00, 0 Fitriana received her master degree from Electrical Engineering Department, Bandung Institute of Technology in 0. She is currently young researcher at Indonesian Institute of Sciences, LIPI Indonesia. Her research interest covers energy/power system tools, power grid integration planning, technical analysis and electrical machines/systems modelling. Nanang Hariyanto was born in Jember, Jawa Timur, Indonesia, on July 6, 96. He graduated from the Electrical Engineering Department, Bandung Institute of Technology. His employment experience included Synatech Industry, and as a researcher at Power System Laboratory, ITB Indonesia. His special fields of interest included power system planning and dynamic stability. 66